Finite Group Databasebeta

← #14640586

Subgroups — #14640586

Order 2816.

210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069597C211yesmaximal, characteristic
2#13066445C211yesmaximal, characteristic
3C11×#1274C211yesmaximal, characteristic
4#10623001C411yescharacteristic
5C11×#431—21no—
6C11×#376C2211yescharacteristic
7#10622538—21no—
8#10622537C411yescharacteristic
9#10622161—21no—
10#10622161—21no—
11C2×C42×C11C2×C411yescharacteristic
12C2×C42×C11D411yescharacteristic
13C2×C42×C11D411yescharacteristic
14#66979—21no—
15#66977—41no—
16C2×#4318—21no—
17#66923C812yescomplemented
18#66922—21no—
19C4×Dic22—41no—
20C11×C4⋊C8—41no—
21C11×C22⋊C8—41no—
22C4×C8×C11—22no—
23C11×#95—41no—
24C22⋊(C11⋊C8)—41no—
25C4⋊(C11⋊C8)—41no—
26C4⋊(C11⋊C8)—41no—
27C4×C11⋊C8—22no—
28#7129—111nomaximal, Sylow
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11—21no—
32C22×C4×C11C22⋊C411yescharacteristic
33C2×Dic22—41no—
34C2×C8×C11—42no—
35C42×C11—21no—
36C42×C11—21no—
37C42×C11—21no—
38C42×C11C2×C811yescharacteristic
39C42×C11M1611yescharacteristic
40C42×C11SD1611yescharacteristic
41C42×C11SD1611yescharacteristic
42C42×C11Q1611yescharacteristic
43C42×C11Q1611yescharacteristic
44C22⋊Dic11—41no—
45C4⋊Dic11—22no—
46C4⋊Dic11—41no—
47Dic11⋊C4—42no—
48C4×Dic11—41no—
49#4318—41no—
50#4318—41no—
51C2×C11⋊C8—42no—
52C2×C11⋊C8—41no—
53#1995—111no—
54#1274—111no—
55#1274D1111yescharacteristic
56C23×C11#9911yescharacteristic
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—81no—
64C2×C4×C11—81no—
65C2×C4×C11—81no—
66C2×C4×C11C22⋊C811yescharacteristic
67C2×C4×C11#10011yescharacteristic
68C2×C4×C11#10311yescharacteristic
69C2×C4×C11#10311yescharacteristic
70C2×C4×C11#10411yescharacteristic
71C2×C4×C11#10411yescharacteristic
72C2×Dic11—42no—
73Dic22—82no—
74C8×C11—82no—
75C11⋊C8—82no—
76C11⋊C8—81no—
77#533—111no—
78#431—21no—
79#431—221no—
80#423—111no—
81#376C2×D1111yescharacteristic
82#339—221no—
83#339—221no—
84C22×C11—41no—
85C22×C11#32311yescharacteristic
86C22×C11#32811yescharacteristic
87C22×C11#32811yescharacteristic
88C4×C11—41no—
89C4×C11—41no—
90C4×C11—41no—
91C4×C11—41no—
92C4×C11—41no—
93C4×C11—41no—
94C4×C11Q8⋊C811yescharacteristic
95C4×C11Q8⋊C811yescharacteristic
96C4×C11#32911yescharacteristic
97C4×C11#33311yescharacteristic
98Dic11—82no—
99C2×M16—221no—
100C4⋊Q8—221no—
101#125—112no—
102C22⋊Q8—441no—
103C4×Q8—441no—
104#117—221no—
105C2×C42C4×D1111yescharacteristic
106C2×C42D4411yescharacteristic
107C2×C42C22⋊D1111yescharacteristic
108C4⋊C8—41no—
109C4⋊C8—441no—
110C4⋊C8—441no—
111C22⋊C8—41no—
112C22⋊C8—441no—
113C4×C8—22no—
114C4×C8—222no—
115#95—41no—
116C2×C11—21no—
117C2×C11—21no—
118C2×C11—21no—
119C2×C11#127211yescharacteristic
120C2×Q8—441no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4(C2×D11)⋊C411yescharacteristic
125M16—441no—
126M16—441no—
127C2×C8—42no—
128C2×C8—442no—
129C2×C8—441no—
130C4⋊C4—222no—
131C4⋊C4—442no—
132C4⋊C4—441no—
133C22⋊C4—441no—
134C42—21no—
135C42—21no—
136C42—21no—
137C42—441no—
138C42C8×D1111yescharacteristic
139C42#431311yescharacteristic
140C42#431411yescharacteristic
141C42Dic4411yescharacteristic
142C42#432411yescharacteristic
143C42#432611yescharacteristic
144C11#712911yescharacteristic, complemented, Sylow
145C23#6687011yescharacteristic
146Q8—882no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4—81no—
156C2×C4—442no—
157C2×C4#6686911yescharacteristic
158C2×C4#6687411yescharacteristic
159C2×C4#6688011yescharacteristic
160C2×C4(C2×D11)⋊C811yescharacteristic
161C2×C4#6688711yescharacteristic
162C2×C4#6688911yescharacteristic
163C8—82no—
164C8—882no—
165C8—881no—
166C22—41no—
167C22#1062209011yescharacteristic
168C22#1062210511yescharacteristic
169C22#1062210611yescharacteristic
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—41no—
175C4—41no—
176C4—882no—
177C4#1062209411yescharacteristic
178C4#1062210211yescharacteristic
179C4#1062211911yescharacteristic
180C4#1062212211yescharacteristic
181C2—21no—
182C2—21no—
183C2—21no—
184C2#1306644111yescharacteristic
subgroupG/H
centerC4#10622102
commutatorC42×C11C2×C8
Frattini#376C2×D11
FittingC11×#1274C2
socleC2×C11#1272
prime radicalC23×C11#99
cosocleC11×#376C22
hypercenter#1274D11
hypocenterC11#7129
LCSG ▷ C42×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #376 ◁ #1274

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
17. #66923C8semidirect
144. C11#7129semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130695972
#130664452
C11×#12742
#712911